Many people have converted their X-frame 1958-'64 Chevy's over to the 1965 and up fully self contained Saginaw 600 series of power steering gear boxes out of mid eighties and newer cars and light trucks. I do not know if they share the same bolt pattern (direct bolt in), but if not the Saginaw 600 box has a flat surface with four lugs that only requires four holes to bolt the gear box to the frame.
Where you will have issues is with the steering column mating to the gear box but I am sure there exist rag joints that will mate the two together. If not you could make one out of the existing parts you have and an old truck tire. (the hoses on the newer boxes are also metric with O-ring seals, but there are adapters for that problem as well).
As stated above the old power assist steering on these cars is just that, an assist. The car has a manual gear box (which takes many turns so that granny Goodwitch has the torque multiplication needed to drive her car to church on Sunday) that has a hydraulic spool valve attached to the input; actuating a hydraulic slave cylinder, so that Granny Goodwitch could parallel park on Monday with just her pinky finger, to buy herself a new pair of lace gloves.
These cars where not designed to be race cars, but soft, smooth riding barges with foam rubber for suspension that wallows with terminal under steer (it was so bad you could peel a tire off the rim in an emergency swerve). If you want to "improve" upon the suspension's handling then I would abandon what Chevy used back in the early sixties as it's design premise is contrary to your intended goal.